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Convert number to sum of different Fibonacci numbers

Convert number to sum of different Fibonacci numbers
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2020-09-26 02:38
FunctionSequenceOptimization
This example demonstrates how to express a number as a sum of different Fibonacci numbers. It involves core mathematical concepts like the Fibonacci sequence and number theory. Construction highlights the use of GeoGebra commands such as Length, Take, Sequence, Textfield, IterationList, If, TableText to achieve Fibonacci decomposition through iteration and conditional logic. Suitable for high school and above students to understand sequence applications and algorithm design.

GeoGebra Commands & Parameters

  1. Length(result) → lenResult
  2. Take(Flatten[Zip[{(a * ""), "+"}, a, result]], 1, (2 * lenResult) - 1) → resultText
  3. Sequence(Sequence[Element[resultText, (nLAfter * j) + k], k, 1, nLAfter], j, 0, floor(Length[resultText] / nLAfter)) → l2
  4. Textfield(n) → InputBox1
  5. IterationList(a + b, a, b, {0, 1}, k) → l1
  6. If(Defined[resultText], TableText[resultText]) → text2
  7. TableText(l2, "lh") → text3

AI Drawing Prompt Reference

Create a graphic that decomposes a number into a sum of different Fibonacci numbers. First, input a number, then generate the Fibonacci sequence through iteration, and finally identify which Fibonacci numbers can be added to form the given number, displaying these terms in an addition format.
The prompt above was compiled from the original drawing commands and is for reference only.